As a wearable electronic device, strain sensor has developed rapidly in recent years, because it is conductive to detecting human movements in various situations. In this study, a new type of highly stretchable and sensitive strain sensor based on electrospun styrene-ethylene-butylene-styrene block copolymer (SEBS) fibrous tubes coated with multi-wall carbon nanotubes (MWCNTs) was reported. The sensor reached a high sensitivity of 3.62 × 105 when the strain was 306%. It also exhibited good stability, repeatability, and durability for different applied strains, different feed speeds, and long-term cyclic loading (15000 cycles). Besides, the sensor could easily be compressed due to its tubular structure and exhibited good response under 0∼29.4 N. Additionally, it showed excellent washing fastness under ultrasonication for 120 min and superior sensing performance in monitoring pulse beat and joint movements. This work provides a new strategy for fabricating strain sensors with high stretchability and high sensitivity. These results demonstrated that the fabricated strain sensor had great potential in smart wearable devices.